Simple answer: yes, you are being abused. In a variety of ways. And he's abusing your children too: name calling and mocking is abuse.
You are walking on eggshells around him, he's successfully trying to coercively control who you spend time with, he is trying to alienate you from your parents/family, he has you in a constant state of anxiety because he's so unpredictable, he's using abusive terminology during arguments, and he's escalating arguments.
All of the above are forms of abuse. And you do not have to put up with them, and you should not permit your children to have to put up with them.
Please seek help immediately. If he abuses you in the meantime - verbally, physically or otherwise, please seek police assistance to make sure you and your kids are safe. If you need friends to come visit and keep you company, or need to go stay with your family and take the children with you then do so - you don't need permission from this f**kwit to so see your family.
I hope it works out for you. Don't let the fact you were in a DV relationship before make you upset now that you are in another one - sadly abusers tend to target nice, kind people to get into relationships with because their victims are far far far better people than they are. If you read about narcissists you'll understand that they are very good at luring people into relationships and then drip drip dripping abuse and control. The "frog in a boiling pot of water" story is a very good one to remember here. It's time for you to get the heck out of that pot!!! And take your little froglets with you!